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Infeasible-interior-point paths are the main tools in interior-point methods for solving many kinds of optimization problems. These paths are usually parametrized by a penalty-parameter r ↓ 0 and further parameters describing their off-centrality and infeasiblilty. Starting with an early result of C. Witzgall et al. [12] in linear programming, this paper gives an overview on results concerning the existence of these paths, their analyticity and the limiting behavior of their derivatives as r ↓ 0, and this also for degenerate problems in the areas of linear programming, linear complementarity problems, and semidefinte programming. [ABSTRACT FROM AUTHOR]

We present two variable metric update methods that have some attractive features: They deal with the problem of finding a least-squares solution of a linear system Ax = b with an m × n-matrix of maximal rank, and can be viewed as a generalization of the DFP- and of the BFGS-methods, respectively, to nonsymmetric matrices A: The methods generate a sequence of n × m-matrices Hk so that the AHk are positive semidefinite and the Hk approximate a right-inverse of A if m ≤ n, and the Moore-Penrose pseudoinverse of A, if m ≥ n. Thus for m = n the methods find approximations to A—1 that could be used as preconditioners in other methods for solving Ax = b when A is not positive definite. Both methods are related to cg-type algorithms minimizing the residual on Krylov-subspaces. [ABSTRACT FROM AUTHOR]

In this paper we derive optimality conditions in the form of a maximum principle for an optimal control problem for nonlinear implicit, or descriptor, control systems. The regularity conditions which are imposed on the system allow us to reduce the optimal control problem to an equivalent nonsmooth variational one. Nonsmooth analysis techniques together with the sliding variations of relaxed controls from optimal control are used to obtain necessary conditions. [ABSTRACT FROM AUTHOR]

Background: There is evidence that acupuncture activates different spinal and supraspinal antinociceptive systems, but the specific modulatory effects on the sensory system have not been systematically investigated. In this study, we evaluated the immediate effects of different types of acupuncture on thermal, mechanical, and vibratory sensory thresholds. Methods: Twenty-four healthy volunteers (12 men and 12 women, mean age 33.1 years) received 3 different forms of acupuncture in a single-blinded crossover design; these included manual acupuncture, acupuncture with low-frequency electrical stimulation, and acupuncture with high-frequency electrical stimulation. The time between the interventions was 1 week. All forms of acupuncture were applied unilaterally in the leg at standard acupuncture points: spleen 6, spleen 9, stomach 36, and gallbladder 39. The effects of acupuncture were evaluated by systematic quantitative sensory testing (QST) immediately after each intervention. QST was performed on bilateral lower extremities, including thermal and mechanical perception and pain and vibratory thresholds. Results: The heat pain threshold was increased after manual acupuncture on the treated and untreated side compared with baseline. Low- and high-frequency electrostimulation led to a higher mechanical pain threshold on the treated side compared with baseline and manual acupuncture. The pressure pain threshold was increased by all forms of acupuncture on both sides, with individual changes from baseline ranging from 25 % to 52 %. Conclusions: There were congruent changes on QST after 3 common acupuncture stimulation methods, with possible unilateral as well as bilateral effects. [ABSTRACT FROM AUTHOR]